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On the Pytkeev property in spaces of continuous functions

Petr Simon, Boaz Tsaban

Published 2006-06-12, updated 2010-11-04Version 5

Answering a question of Sakai, we show that the minimal cardinality of a set of reals X such that C_p(X) does not have the Pytkeev property is equal to the pseudo-intersection number p. Our approach leads to a natural characterization of the Pytkeev property of C_p(X) by means of a covering property of X, and to a similar result for the Reznicenko property of C_p(X).

Journal: Proceedings of the American Mathematical Society 136 (2008), 1125-1135
Categories: math.GN, math.CO, math.LO
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